In Appendix II, empirical and approximate formulas and other applications for which the codes ALESQ and TSOLVE were used are listed the results are mostly related to the field of radiation physics. In Appendix I, procedures and methods to formulate empirical equations are discussed. The codes published originally in 1984 assumed the use of main-frame computers, and those in the present edition have been modified for the use on desk-top computers with some additional improvements. Both ALESQ and TSOLVE can also be used for linear problems. A routine to estimate tolerances for roundoff of the solution has been developed and included in TSOLVE. The code for this algorithm is called TSOLVE. The algorithm used for the best approximation is basically the one developed by Osborne and Watson a method to obtain the solution for the continuous best-approximation problem with a discrete set of data has been incorporated. the equation to the data with approximately equal relative uncertainties, a two-step method is proposed, and conveniences for this method are provided in ALESQ. The code for this algorithm is called ALESQ. The algorithm used for the least-squares fit is based on the maximum neighborhood algorithm developed by Levenberg and Marquardt an improvement in strategy proposed by the present authors has been incorporated. In Appendix II, empirical- and approximate formulas and other applications for which the codes ALESQ and TSOLVE were used are listed the results are mostly related to the field of radiation physics.Īlgorithms for nonlinear least-squares fit and best approximation are described, and FORTRAN codes for these algorithms are given. For fitting the equation to the data with approximately equal relative uncertainties, a two-step method is proposed, and conveniences for this method are provided in ALESQ. Algorithms for nonlinear least-squares fit and best approximation are described, and FORTRAN codes for these algorithms are given.
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